Answer
$b=2$
Work Step by Step
The given equation is
$\Rightarrow \sqrt {b+7}-5=-2$
Add $5$ to each side.
$\Rightarrow \sqrt {b+7}-5+5=-2+5$
Simplify.
$\Rightarrow \sqrt {b+7}=3$
Square each side of the equation.
$\Rightarrow (\sqrt{b+7})^2=3^2$
Simplify.
$\Rightarrow b+7=9$
Subtract $7$ from each side.
$\Rightarrow b+7-7=9-7$
Simplify.
$\Rightarrow b=2$
Check $b=2$.
$\Rightarrow \sqrt {b+7}-5=-2$
$\Rightarrow \sqrt {2+7}-5=-2$
$\Rightarrow \sqrt {9}-5=-2$
$\Rightarrow \sqrt {3^2}-5=-2$
$\Rightarrow 3-5=-2$
$\Rightarrow -2=-2$
True.
Hence, the solution is $b=2$.
